A note on the optimality of index priority rules for search and sequencing problems

We show that the linear objective function of a search problem can be generalized to a power function and/or a logarithmic function and still be minimized by an index priority rule. We prove our result by solving the differential equation resulting from the required invariance condition, therefore, we also prove that any other generalization of this linear objective function will not lead to an index priority rule. We also demonstrate the full equivalence between two related search problems in the sense that a solution to either one can be used to solve the other one and vice versa. Finally, we show that the linear function is the only function leading to an index priority rule for the single‐machine makespan minimization problem with deteriorating jobs and an additive job deterioration function. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

A heuristic for maximizing the number of on‐time jobs on two uniform parallel machines

We consider the problem of maximizing the number of on‐time jobs on two uniform parallel machines. We show that a straightforward extension of an algorithm developed for the simpler two identical parallel machines problem yields a heuristic with a worst‐case ratio bound of at least . We then show that the infusion of a “look ahead” feature into the aforementioned algorithm results in a heuristic with the tight worst‐case ratio bound of , which, to our knowledge, is the tightest worst‐case ratio bound available for the problem. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

The fixed charge problem

A fundamental unsolved problem in the programming area is one in which various activities have fixed charges (e.g., set-up time charges) if operating at a positive level. Properties of a general solution to this type problem are discussed in this paper. Under special circumstances it is shown that a fixed charge problem can be reduced to an ordinary linear programming problem.     

Programming the procurement of airlift and sealift forces: A linear programming model for analysis of the least-cost mix of strategic deployment systems

A linear programming model for analyzing the strategic deployment mix of airlift and sealift forces and prepositioning to accomplish the composite requirements of a set of possible contingencies is described in this paper. It solves for the least-cost mix of deployment means capable of meeting any one of a spectrum of contingencies, or meeting simultaneous contingencies. The model was developed by RAC as part of the U.S. Army's study program and has been used in analyses of deployment systems conducted in support of the U.S. Army, the Joint Chiefs of Staff and the Office of the Secretary of Defense. Results of analyses have influenced the preparation of long-range plans as well as the formulation of the FY67 Department of Defense budget. The paper gives the background and assumptions of the model, describes the model by means of a simple hypothetical example followed by a selected subset of a complete version, and discusses how the model is used.     

Incorporation dynamic aspects and uncertainty in 1‐median location problems

In this paper we present several 1‐median formulations on a tree network which incorporate dynamic evolution and/or uncertainty of node demands and transportation costs over a planning horizon. Dynamic evolution is modeled using linear demand functions for the nodes and linear length functions for the edges. Uncertainty is modeled with the use of multiple scenarios, where a scenario is a complete specification of the uncertain node demands and/or edge lengths. We formulate our objective using minimax regret like criteria. We use two different criteria, namely, robust deviation and relative robustness. We discuss what motivated the introduction of these objectives, as well as their relation to existing literature and decision making practices. For all of the models presented, we provide low‐order polynomial time algorithms. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 147–168, 1999